Determining instantaneous velocity from a graph

In summary, the problem with the homework statement is that the graph is terrible and the numbers are not very well set.
  • #1
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Homework Statement


This is how my problem has been presented:
The position of a rabbit along a straight tunnel as a function of time is plotted in Fig. 2-26.

http://img134.imageshack.us/img134/8263/graphxt5.th.jpg http://g.imageshack.us/thpix.php

Determine its instantaneous velocity at the following times.

(b) t = 32.5 s

2. The attempt at a solution

Attempts are:
0.49231 m/s
0.50769 m/s
0.523077 m/s
0.53846 m/s
0.553846 m/s
0.56923 m/s
0.57085 m/s
0.5846 m/s

The numbers are obtained, though rounded, for x/32.5 s, where x is, and in order:
16
16.5
17
17.5
18
18.5
18.552625 (obtained by count pixels and some math to get a number, though it failed)
19

The problem is probably just because the graph is terrible for this kind of work, due to the fact that the graph came off some different problem that was intended for students to describe the graph, so the numbers aren't very well set.

These are the numbers I obtained off the few weeks of physics I had but any other input is fine.
Its also fine to give a guess off the top of your head, so i can try it, but please base it off something.
 
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  • #2
To find instentanious velocity just draw a tangent to the graph at that specific time and calculate the tangents slope
 
  • #3
So just to be sure, it would be a line from a point (I used 0,0) through tangent to the point at 32.5s (which would be the middle of the line, since it is about 5 pixels wide).

Also that it would look like this picture, more or less.

http://img515.imageshack.us/img515/2900/graph2mg6.th.jpg http://g.imageshack.us/thpix.php

If so, then I do get a new number, 0.57143 m/s at 18.57 m.

Thanks for your input.
 
Last edited by a moderator:
  • #4
Yes that would roughly be it. However I think the tangent line should be a bit higher.
 

1. How is instantaneous velocity defined?

Instantaneous velocity is defined as the rate of change of an object's position at a specific moment in time. It is the slope of the tangent line to the position-time graph at that point.

2. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time, while instantaneous velocity is the velocity at a specific moment in time. Average velocity is calculated over an interval, whereas instantaneous velocity is calculated at a specific point.

3. How can you determine instantaneous velocity from a position-time graph?

Instantaneous velocity can be determined by finding the slope of the tangent line to the position-time graph at a specific point. This can be done by drawing a line that just touches the curve at that point and calculating its slope using the rise over run method.

4. Can instantaneous velocity be negative?

Yes, instantaneous velocity can be negative. This means the object is moving in the negative direction on the position-time graph.

5. How does the shape of a position-time graph affect the instantaneous velocity?

The shape of a position-time graph can affect the instantaneous velocity by changing the slope of the tangent line at different points. A steeper slope indicates a higher instantaneous velocity, while a flatter slope indicates a lower instantaneous velocity.

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